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Simplifying (5x2 + -20) + (4x + -25) = 180 Reorder the terms: (-20 + 5x2) + (4x + -25) = 180 Remove parenthesis around (-20 + 5x2) -20 + 5x2 + (4x + -25) = 180 Reorder the terms: -20 + 5x2 + (-25 + 4x) = 180 Remove parenthesis around (-25 + 4x) -20 + 5x2 + -25 + 4x = 180 Reorder the terms: -20 + -25 + 4x + 5x2 = 180 Combine like terms: -20 + -25 = -45 -45 + 4x + 5x2 = 180 Solving -45 + 4x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: -45 + -180 + 4x + 5x2 = 180 + -180 Combine like terms: -45 + -180 = -225 -225 + 4x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -225 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -45 + 0.8x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 0.8x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 0.8x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 0.8x + x2 = 0 + 45 0.8x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 0.8x + x2 = 45 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 45 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 45 + 0.16 Combine like terms: 45 + 0.16 = 45.16 0.16 + 0.8x + x2 = 45.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 45.16 Calculate the square root of the right side: 6.720119047 Break this problem into two subproblems by setting (x + 0.4) equal to 6.720119047 and -6.720119047.Subproblem 1
x + 0.4 = 6.720119047 Simplifying x + 0.4 = 6.720119047 Reorder the terms: 0.4 + x = 6.720119047 Solving 0.4 + x = 6.720119047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 6.720119047 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 6.720119047 + -0.4 x = 6.720119047 + -0.4 Combine like terms: 6.720119047 + -0.4 = 6.320119047 x = 6.320119047 Simplifying x = 6.320119047Subproblem 2
x + 0.4 = -6.720119047 Simplifying x + 0.4 = -6.720119047 Reorder the terms: 0.4 + x = -6.720119047 Solving 0.4 + x = -6.720119047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -6.720119047 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -6.720119047 + -0.4 x = -6.720119047 + -0.4 Combine like terms: -6.720119047 + -0.4 = -7.120119047 x = -7.120119047 Simplifying x = -7.120119047Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.320119047, -7.120119047}
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